How did they get from the second expression to the third? (simplification)

**kingsolomonsgrave** · November 14th 2012, 10:26 AM

How did they get from the second expression to the third?

It was stated earlier in this problem that radius r=cube root of (500/Pi) so that's why it's equal to 2r but I don't understand the simplification from 1000/Pi(500/Pi)^(2/3) to the next expression.

**skeeter** · November 14th 2012, 10:48 AM

$\frac{1000}{\pi \left(\frac{500}{\pi}\right)^{2/3}} =$

$\frac{1000}{\pi} \cdot \frac{\pi^{2/3}}{500^{2/3}} =$

$\frac{2 \cdot 500}{\pi} \cdot \frac{\pi^{2/3}}{500^{2/3}} =$

$\frac{2 \cdot 500^{1/3}}{\pi^{1/3}} = 2\sqrt[3]{\frac{500}{\pi}}$

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How did they get from the second expression to the third? (simplification)

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